calculus

[ACLerok]

i need some help badly on this.. ive never taken calc before so i have no clue. any suggestions, tips, hints, or anything of value is SO greatly appreciated. thank you alot!

http://www.eden.rutgers.edu/~cjjacob/images/calc.gif

[Hurkyl]

Well, let's start with part (a).

Have you sketched the graph of T, yet? Can you tell me what a limit is, intuitively?

[ACLerok]

a limit is a number or point L that is approached by a function f(x) as x approaches a. i do not understand how to graph it.

[Hurkyl]

Do you know how to graph the function S?

[ACLerok]

yeah

[Hurkyl]

Ok, so T and S are the same everywhere, except at the point where x = 3, right?

So everywhere except at x = 3, the graph of T looks exactly like the graph of S... so graph that... then plot the point corresponding to x = 3.

Got this part so far?


p.s. when there is a point missing on a curve, it is the usual convention to mark it by drawing a tiny circle around the missing point, and not drawing the curve through the circle.

[ACLerok]

Originally posted by Hurkyl
Ok, so T and S are the same everywhere, except at the point where x = 3, right?

So everywhere except at x = 3, the graph of T looks exactly like the graph of S... so graph that... then plot the point corresponding to x = 3.

Got this part so far?


p.s. when there is a point missing on a curve, it is the usual convention to mark it by drawing a tiny circle around the missing point, and not drawing the curve through the circle.

I think im understanding it a little better now. The graph of S is a parabola, correct? So the graph of T will look exactly like S except at the point x=3? But what will the point at 3 look like? An open circle? What about T(x)=7 if x=3? should i graph a point a 7?
And I still do not understand how to find the limits it tells me to find. They expect us to do these problems in worshop yet we're still going over precalc in lecture! Oh well, I hope you guy/gals can help me out. Thanks alot!

[Hurkyl]

What about T(x)=7 if x=3? should i graph a point a 7?

Right, you'd plot a point at (3, 7)

(and a little open circle at (3, 9) to show that there is not supposed to be a point there)


And I still do not understand how to find the limits it tells me to find.

I get the impression they want you to argue intuitively for the moment. So you know a limit is

a limit is a number or point L that is approached by a function f(x) as x approaches a. i do not understand how to graph it.

So tell me, what does T(x) seem to approach as x approaches 5? As x approaches 3?

(and note the values at 5 and 3 don't matter; just the values as you approach 5 and 3)

[ACLerok]

Originally posted by Hurkyl
Right, you'd plot a point at (3, 7)

(and a little open circle at (3, 9) to show that there is not supposed to be a point there)




I get the impression they want you to argue intuitively for the moment. So you know a limit is



So tell me, what does T(x) seem to approach as x approaches 5? As x approaches 3?

(and note the values at 5 and 3 don't matter; just the values as you approach 5 and 3)

so will the graph of T look sort of like a W shape?
i tried finding the limits as x approaches 5 and came up with 25 and as x approaches 3 i got 9. What do you think?

[Hurkyl]

so will the graph of T look sort of like a W shape?

Nope; the graph of T looks like a parabola that has a hole at (3, 9), and an extra point at (3, 7).

The graph is not a connected one; maybe that's what's confusing you?


I think your limits are correct. Do you have a guess as to part (b)?

[ACLerok]

umm. does the parabola go through (3,9) but with a hole? just curious if im doing right. how do you know theres a hole at (3,9)?
i think for part B that as x approaches a, the limit will be a but im not quite sure how to explain since i find this problem to be quite vague.. what do you think? and BTW thanks.

[Hurkyl]

does the parabola go through (3,9) but with a hole?

Yep

how do you know theres a hole at (3,9)?

Well, I know the parabola (given by S) goes through the point (3, 9), because S(3) = 9.

However, I know that T disagrees with S when x = 3, so the point corresponding to x = 3 (that is, the point (3, 9)) is a "hole" in the parabola.


I think for part B that as x approaches a, the limit will be a

(I'm not sure if you made a typo)

Well, you've already (essentially) solved the case where the evil alien only changed a single point of S(x). [:)] The thing to realize from part (a) is that whenever the evil alien changes a single point, limits are not affected. So when the alien changes a million points (which can be done 1 at a time), the values of limits are the same as if nothing was changed!

[ACLerok]

Thanks alot! You may hear from me again next week with another problem but lets hope not! :)
Thanks again!